|It doesn't sound like it's a problem with the wiring but just to make sure you might try another pair of headphones and see if they act the same.|
Just a guess but is it possible windows is cutting power to that port? They're coming up with all kinds of ways to reduce power consumption in laptops. I know they do that already with USB ports. Since it's doing it during hibernation and when the battery is low maybe that's what's going on. Youi might be able to check that either in device manager or sound devices in control panel.
DAVEINCAPS - Made with REAL high fructose corn syrup.